[Summation Notation] Use Sigma Notation to write the following sums.

Question

0

2114

1

+69

Use Sigma Notation to write the following sums.

a) 1/4 + 3/8 + 7/16 + 15/32 + 31/64

b) 1/2+ 2/4 + 6/8 + 24/16 + 120/32 + 720/64

(Note: Any tips or methods in finding the answer are much apreciated)

fizzworth May 22, 2016

+118696

+10

Best Answer

a) 1/4 + 3/8 + 7/16 + 15/32 + 31/64

I noticed that the differentces in the numerator were 2, 4, 8, 16 and these are powers of 2. So...

$\displaystyle\sum_{n=1}^{n=5}\;\frac{2^n-1}{2^{n+1}}$

b) 1/2+ 2/4 + 6/8 + 24/16 + 120/32 + 720/64

$\displaystyle\sum_{n=1}^{n=6}\;\frac{n!}{2^n}$

Melody May 23, 2016

Melody · Answer 1 · 2016-05-23T02:21:30

a) 1/4 + 3/8 + 7/16 + 15/32 + 31/64

I noticed that the differentces in the numerator were 2, 4, 8, 16 and these are powers of 2. So...

$\displaystyle\sum_{n=1}^{n=5}\;\frac{2^n-1}{2^{n+1}}$

b) 1/2+ 2/4 + 6/8 + 24/16 + 120/32 + 720/64

$\displaystyle\sum_{n=1}^{n=6}\;\frac{n!}{2^n}$